RS4D: Multi-Domain 4D Sensing

• RS4D is a domain-dependent label that encompasses distinct 4D sensing approaches in remote sensing, mobile sensing, and detector physics.
• In remote and mobile sensing, it leverages efficient state space models and Butterworth filtering to reduce computational complexity and enhance noise robustness.
• In detector physics, RS4D employs Resistive Silicon (AC-LGAD) to achieve high spatial-temporal precision in tracking, offering improved accuracy and reduced resource demands.

RS4D is a domain-dependent research label rather than a single established technical term. In current arXiv usage, it denotes at least three distinct constructs: a remote sensing instance segmentation framework based on distilled state space models; a “robust S4D” long-sequence decoder for mobile sensing; and a Resistive Silicon for 4D tracking concept built around RSD or AC-LGAD sensors. In adjacent literatures, the same string also appears as an informal shorthand for RSTAR4D in respiration-resolved cone-beam CT and as a task-level shorthand for 4D radar super-resolution. The term therefore requires explicit disambiguation by field, architecture, and measurement modality (Yang et al., 24 Jun 2026, Mei et al., 2024, Deng et al., 2024, Zheng et al., 21 Mar 2025, Arcidiacono et al., 2022).

1. Terminological scope

The identifier RS4D is used in several distinct research contexts. Some usages are formal method names, while others are informal aliases or umbrella labels.

Domain	Meaning of “RS4D”	Representative source
Remote sensing	Linear-time instance segmentation with distilled SSM backbones	(Yang et al., 24 Jun 2026)
Mobile sensing	“robust S4D” sequence model with Butterworth-initialized filtering	(Mei et al., 2024)
4D tracking detectors	Resistive Silicon for 4D tracking using RSD or AC-LGAD	(Arcidiacono et al., 2022)
4D CBCT	Informal alias for RSTAR4D-Net	(Deng et al., 2024)
4D radar SR	Task-level shorthand for 4D radar super-resolution	(Zheng et al., 21 Mar 2025)

Two distinctions are especially important. First, RS4D is explicit and primary in the remote sensing and mobile sensing papers. Second, in the 4D CBCT and 4D radar super-resolution literatures, the label is secondary: the CBCT paper names the method RSTAR or RSTAR-Net and notes that “RS4D” is an informal shorthand referring to the same approach, while the radar paper states that RS4D typically denotes 4D radar super-resolution even though the proposed framework itself is named R2LDM (Deng et al., 2024, Zheng et al., 21 Mar 2025).

2. RS4D in remote sensing instance segmentation

In remote sensing, RS4D is a method for instance segmentation that replaces quadratic-cost Transformer token mixing with linear-time state space modeling. The formulation is motivated by dense prediction on very high resolution images, where a ViT backbone incurs self-attention complexity $O(N^2 d)$, whereas the SSM backbone operates at $O(N d)$ time and $O(N)$ memory. The method distills segmentation priors from a SAM visual encoder, specifically a ViT-Base teacher pretrained on SA-1B, into lightweight student backbones through adaptive noise and masking knowledge distillation (Yang et al., 24 Jun 2026).

The architecture explores three student backbones: VanillaMamba, TransMamba, and ScanningMamba. VanillaMamba uses 12 stacked Vision Mamba blocks; TransMamba uses 12 TRViM hybrid layers without self-attention; ScanningMamba, the default configuration, uses 24 stacked blocks with bidirectional scanning:

$$X_\mathrm{back} = \mathrm{Mambamixer}(\mathrm{flip}(X_{c-1})),\quad X_\mathrm{fwd} = \mathrm{Mambamixer}(X_{c-1}),\quad X_c = X_{c-1} + (X_\mathrm{back} + \mathrm{flip}(X_\mathrm{fwd}))/2.$$

The neck reshapes selected sequence features into multi-scale maps using down-sampled feature layers, cascaded residuals, and a SimpleFPN. Two segmentation heads are evaluated: a Mask R-CNN-style “RS4D (box)” head and a SAM-style “RS4D (prompt)” head (Yang et al., 24 Jun 2026).

Distillation uses masked and noisy student inputs while the teacher receives clean $1024\times1024$ images. The feature-level distillation loss is

$$L_\mathrm{kd} = \frac{1}{b\,l\,d}\sum_{j=1}^{b}\sum_{i=1}^{l} \big\|y^{T}_{ij} - y^{S}_{ij}\big\|_{1},$$

and the adaptive corruption is defined by

$$X' = \mathrm{mask}(X_\mathrm{input}) + \epsilon\,\delta,\quad \delta \sim \mathrm{Uniform}(0,1),\quad \epsilon = \min\big(\max_{b,l,d}(|Y_{e-1}|),A_\mathrm{const}\big).$$

Mask ratios of $0\%$, $10\%$, $20\%$, and $O(N d)$0 are studied, with the ablations reporting that performance is optimal around $O(N d)$1 noise and $O(N d)$2 masking. Fine-tuning uses AdamW with initial learning rate $O(N d)$3, weight decay $O(N d)$4, cosine annealing with linear warmup, bfloat16 precision, and 800 epochs (Yang et al., 24 Jun 2026).

The reported efficiency gains are central to this usage of RS4D. At $O(N d)$5, the student SSM backbone has approximately $O(N d)$6M parameters and $O(N d)$7G FLOPs, compared with $O(N d)$8M parameters and $O(N d)$9G FLOPs for the ViT-Base teacher backbone. The paper summarizes this as about $O(N)$0 fewer backbone parameters and $O(N)$1 fewer FLOPs, with GPU memory usage reduced by $O(N)$2 at $O(N)$3 relative to ViT-based RSPrompter (Yang et al., 24 Jun 2026).

On SSDD, RS4D (box) reports $O(N)$4 and $O(N)$5, with $O(N)$6 and $O(N)$7. On WHU, RS4D (box) reports $O(N)$8 and $O(N)$9. On NWPU, RS4D (box) reports $$X_\mathrm{back} = \mathrm{Mambamixer}(\mathrm{flip}(X_{c-1})),\quad X_\mathrm{fwd} = \mathrm{Mambamixer}(X_{c-1}),\quad X_c = X_{c-1} + (X_\mathrm{back} + \mathrm{flip}(X_\mathrm{fwd}))/2.$$0 and $$X_\mathrm{back} = \mathrm{Mambamixer}(\mathrm{flip}(X_{c-1})),\quad X_\mathrm{fwd} = \mathrm{Mambamixer}(X_{c-1}),\quad X_c = X_{c-1} + (X_\mathrm{back} + \mathrm{flip}(X_\mathrm{fwd}))/2.$$1. ScanningMamba is identified as the fastest and most stable backbone variant, and multiple intermediate layers in the neck yield better mask AP than using only the final layer (Yang et al., 24 Jun 2026).

3. RS4D as robust S4D in mobile sensing

In mobile sensing, RS4D denotes “robust S4D,” a state-space-based recurrent architecture for reconstructing high-dimensional spatio-temporal fields from sparse, mobile sensor measurements. The core idea is to prepend a filtering S4D layer, initialized as a Butterworth low-pass filter, before standard S4D memorization layers. This front-end suppresses high-frequency measurement noise before long-range state propagation, and the resulting recurrent block is integrated into a shallow decoder network (Mei et al., 2024).

The underlying continuous-time state space model is

$$X_\mathrm{back} = \mathrm{Mambamixer}(\mathrm{flip}(X_{c-1})),\quad X_\mathrm{fwd} = \mathrm{Mambamixer}(X_{c-1}),\quad X_c = X_{c-1} + (X_\mathrm{back} + \mathrm{flip}(X_\mathrm{fwd}))/2.$$2

with convolution kernel

$$X_\mathrm{back} = \mathrm{Mambamixer}(\mathrm{flip}(X_{c-1})),\quad X_\mathrm{fwd} = \mathrm{Mambamixer}(X_{c-1}),\quad X_c = X_{c-1} + (X_\mathrm{back} + \mathrm{flip}(X_\mathrm{fwd}))/2.$$3

S4D uses diagonal parameterization of $$X_\mathrm{back} = \mathrm{Mambamixer}(\mathrm{flip}(X_{c-1})),\quad X_\mathrm{fwd} = \mathrm{Mambamixer}(X_{c-1}),\quad X_c = X_{c-1} + (X_\mathrm{back} + \mathrm{flip}(X_\mathrm{fwd}))/2.$$4, with HiPPO-inspired initializations such as

$$X_\mathrm{back} = \mathrm{Mambamixer}(\mathrm{flip}(X_{c-1})),\quad X_\mathrm{fwd} = \mathrm{Mambamixer}(X_{c-1}),\quad X_c = X_{c-1} + (X_\mathrm{back} + \mathrm{flip}(X_\mathrm{fwd}))/2.$$5

After zero-order-hold discretization,

$$X_\mathrm{back} = \mathrm{Mambamixer}(\mathrm{flip}(X_{c-1})),\quad X_\mathrm{fwd} = \mathrm{Mambamixer}(X_{c-1}),\quad X_c = X_{c-1} + (X_\mathrm{back} + \mathrm{flip}(X_\mathrm{fwd}))/2.$$6

The diagonal structure produces a Vandermonde-form discrete kernel and efficient long-sequence processing (Mei et al., 2024).

The robust component is the Butterworth-initialized S4D-BW layer. For an $$X_\mathrm{back} = \mathrm{Mambamixer}(\mathrm{flip}(X_{c-1})),\quad X_\mathrm{fwd} = \mathrm{Mambamixer}(X_{c-1}),\quad X_c = X_{c-1} + (X_\mathrm{back} + \mathrm{flip}(X_\mathrm{fwd}))/2.$$7th-order analog Butterworth low-pass filter,

$$X_\mathrm{back} = \mathrm{Mambamixer}(\mathrm{flip}(X_{c-1})),\quad X_\mathrm{fwd} = \mathrm{Mambamixer}(X_{c-1}),\quad X_c = X_{c-1} + (X_\mathrm{back} + \mathrm{flip}(X_\mathrm{fwd}))/2.$$8

and the poles are

$$X_\mathrm{back} = \mathrm{Mambamixer}(\mathrm{flip}(X_{c-1})),\quad X_\mathrm{fwd} = \mathrm{Mambamixer}(X_{c-1}),\quad X_c = X_{c-1} + (X_\mathrm{back} + \mathrm{flip}(X_\mathrm{fwd}))/2.$$9

The paper maps these poles into diagonal S4D initialization, with the effective cutoff controlled by the learned discretization step $1024\times1024$0. The resulting RS4D stack comprises one S4D-BW layer followed by one or more S4D-Lin layers, with a shallow MLP decoder producing the reconstructed state field (Mei et al., 2024).

The empirical profile is task-dependent. On the double gyre benchmark, RMSE is $1024\times1024$1 for RS4D versus $1024\times1024$2 for S4D and $1024\times1024$3 for LSTM in the noise-free case; under a disturbed last step, RS4D reports $1024\times1024$4 versus $1024\times1024$5 for S4D and $1024\times1024$6 for LSTM; under noisy inputs, RS4D reports $1024\times1024$7 versus $1024\times1024$8 for S4D and $1024\times1024$9 for LSTM. On HYCOM sea surface temperature, RS4D achieves the best validation RMSE across the Global, West Pacific, and South Atlantic regions, with values $$L_\mathrm{kd} = \frac{1}{b\,l\,d}\sum_{j=1}^{b}\sum_{i=1}^{l} \big\|y^{T}_{ij} - y^{S}_{ij}\big\|_{1},$$0, $$L_\mathrm{kd} = \frac{1}{b\,l\,d}\sum_{j=1}^{b}\sum_{i=1}^{l} \big\|y^{T}_{ij} - y^{S}_{ij}\big\|_{1},$$1, and $$L_\mathrm{kd} = \frac{1}{b\,l\,d}\sum_{j=1}^{b}\sum_{i=1}^{l} \big\|y^{T}_{ij} - y^{S}_{ij}\big\|_{1},$$2, respectively. On Kolmogorov flow, validation RMSE is $$L_\mathrm{kd} = \frac{1}{b\,l\,d}\sum_{j=1}^{b}\sum_{i=1}^{l} \big\|y^{T}_{ij} - y^{S}_{ij}\big\|_{1},$$3 for RS4D versus $$L_\mathrm{kd} = \frac{1}{b\,l\,d}\sum_{j=1}^{b}\sum_{i=1}^{l} \big\|y^{T}_{ij} - y^{S}_{ij}\big\|_{1},$$4 for S4D and $$L_\mathrm{kd} = \frac{1}{b\,l\,d}\sum_{j=1}^{b}\sum_{i=1}^{l} \big\|y^{T}_{ij} - y^{S}_{ij}\big\|_{1},$$5 for LSTM. On detonation waves, validation RMSE is $$L_\mathrm{kd} = \frac{1}{b\,l\,d}\sum_{j=1}^{b}\sum_{i=1}^{l} \big\|y^{T}_{ij} - y^{S}_{ij}\big\|_{1},$$6 for RS4D versus $$L_\mathrm{kd} = \frac{1}{b\,l\,d}\sum_{j=1}^{b}\sum_{i=1}^{l} \big\|y^{T}_{ij} - y^{S}_{ij}\big\|_{1},$$7 for S4D and $$L_\mathrm{kd} = \frac{1}{b\,l\,d}\sum_{j=1}^{b}\sum_{i=1}^{l} \big\|y^{T}_{ij} - y^{S}_{ij}\big\|_{1},$$8 for LSTM (Mei et al., 2024).

The paper also reports that RS4D reduces disturbance sensitivity and improves convergence speed and consistency relative to vanilla S4D and LSTM. A plausible implication is that, in this usage, “RS4D” emphasizes noise-robust long-memory sequence modeling rather than 4D sensing in the imaging or detector sense.

4. Informal RS4D usages in 4D imaging and 4D radar

In respiration-resolved cone-beam CT, “RS4D” is an informal alias for RSTAR4D-Net, the method introduced in “RSTAR4D: Rotational Streak Artifact Reduction in 4D CBCT using a Separable 4D CNN” (Deng et al., 2024). The paper attributes the key artifact mechanism to sparse, phase-specific sampling: a single one-minute full-rotation scan is sorted into respiratory phase bins, each phase image $$L_\mathrm{kd} = \frac{1}{b\,l\,d}\sum_{j=1}^{b}\sum_{i=1}^{l} \big\|y^{T}_{ij} - y^{S}_{ij}\big\|_{1},$$9 is reconstructed from a small and unevenly distributed subset of projections $$X' = \mathrm{mask}(X_\mathrm{input}) + \epsilon\,\delta,\quad \delta \sim \mathrm{Uniform}(0,1),\quad \epsilon = \min\big(\max_{b,l,d}(|Y_{e-1}|),A_\mathrm{const}\big).$$0, and the resultant discontinuities generate severe streak artifacts. The average image is

$$X' = \mathrm{mask}(X_\mathrm{input}) + \epsilon\,\delta,\quad \delta \sim \mathrm{Uniform}(0,1),\quad \epsilon = \min\big(\max_{b,l,d}(|Y_{e-1}|),A_\mathrm{const}\big).$$1

and Fourier-space analysis shows that the streaks rotate regularly across respiratory phases. This motion is termed rotational streak artifacts, or RSA, and is described as distinct from diaphragm-driven respiratory motion. The proposed network processes the entire phase series jointly with separable spatiotemporal convolutions, grouped convolution, and circular temporal padding. On simulated data, RSTAR-Net reports the best scores among the compared methods: SSIM-Global $$X' = \mathrm{mask}(X_\mathrm{input}) + \epsilon\,\delta,\quad \delta \sim \mathrm{Uniform}(0,1),\quad \epsilon = \min\big(\max_{b,l,d}(|Y_{e-1}|),A_\mathrm{const}\big).$$2, PSNR-Global $$X' = \mathrm{mask}(X_\mathrm{input}) + \epsilon\,\delta,\quad \delta \sim \mathrm{Uniform}(0,1),\quad \epsilon = \min\big(\max_{b,l,d}(|Y_{e-1}|),A_\mathrm{const}\big).$$3, SSIM-Lung $$X' = \mathrm{mask}(X_\mathrm{input}) + \epsilon\,\delta,\quad \delta \sim \mathrm{Uniform}(0,1),\quad \epsilon = \min\big(\max_{b,l,d}(|Y_{e-1}|),A_\mathrm{const}\big).$$4, and PSNR-Lung $$X' = \mathrm{mask}(X_\mathrm{input}) + \epsilon\,\delta,\quad \delta \sim \mathrm{Uniform}(0,1),\quad \epsilon = \min\big(\max_{b,l,d}(|Y_{e-1}|),A_\mathrm{const}\big).$$5 (Deng et al., 2024).

In 4D radar super-resolution, the paper “R2LDM: An Efficient 4D Radar Super-Resolution Framework Leveraging Diffusion Model” states that RS4D typically denotes 4D radar super-resolution, although the proposed method is named R2LDM rather than RS4D (Zheng et al., 21 Mar 2025). Here the task is to densify sparse and noisy mmWave radar point clouds into LiDAR-like point clouds while preserving scene geometry. R2LDM uses voxel features rather than range images or BEV images, a latent voxel diffusion model for conditional denoising, and a Latent Point Cloud Reconstruction module that predicts occupancy masks and voxel offsets. The method reports $$X' = \mathrm{mask}(X_\mathrm{input}) + \epsilon\,\delta,\quad \delta \sim \mathrm{Uniform}(0,1),\quad \epsilon = \min\big(\max_{b,l,d}(|Y_{e-1}|),A_\mathrm{const}\big).$$6- to $$X' = \mathrm{mask}(X_\mathrm{input}) + \epsilon\,\delta,\quad \delta \sim \mathrm{Uniform}(0,1),\quad \epsilon = \min\big(\max_{b,l,d}(|Y_{e-1}|),A_\mathrm{const}\big).$$7-fold densification of radar point clouds, up to $$X' = \mathrm{mask}(X_\mathrm{input}) + \epsilon\,\delta,\quad \delta \sim \mathrm{Uniform}(0,1),\quad \epsilon = \min\big(\max_{b,l,d}(|Y_{e-1}|),A_\mathrm{const}\big).$$8 improvement in point cloud registration recall rate, and up to $$X' = \mathrm{mask}(X_\mathrm{input}) + \epsilon\,\delta,\quad \delta \sim \mathrm{Uniform}(0,1),\quad \epsilon = \min\big(\max_{b,l,d}(|Y_{e-1}|),A_\mathrm{const}\big).$$9 improvement in object detection accuracy. On GPAL, it improves Chamfer Distance from $0\%$0 for R2DM to $0\%$1, Hausdorff Distance from $0\%$2 to $0\%$3, and F-Score from $0\%$4 to $0\%$5 (Zheng et al., 21 Mar 2025).

These two usages are terminologically adjacent rather than nominally identical. In the CBCT case, RS4D refers informally to a specific artifact-reduction network. In the radar case, RS4D refers to the task area of 4D radar super-resolution, within which R2LDM is presented as a state-of-the-art framework.

5. RS4D as Resistive Silicon for 4D tracking

In detector physics, RS4D stands for Resistive Silicon for 4D tracking. The enabling device technology is the Resistive Silicon Detector, also called AC-LGAD, which combines a thin LGAD multiplication layer, an unsegmented n+ resistive sheet, and AC-coupled metal electrodes. The resistive sheet produces built-in charge sharing across multiple pads, while the LGAD gain preserves precise timing. This arrangement is designed to achieve simultaneous space and time measurements with large pixels and 100% fill factor (Arcidiacono et al., 2022).

The reconstruction formalism in this literature is explicit. For four-pad position measurement, the signal-weighted position estimator is

$0\%$6

and the discretized position circuit estimator is

$0\%$7

Time combination across pads is derived from a weighted $0\%$8 minimization, yielding

$0\%$9

The spatial and timing error models are likewise decomposed into jitter, reconstruction, setup, sensor, Landau, and delay terms (Arcidiacono et al., 2022).

Experimentally, the 2022 TCT study on FBK RSD2 sensors reports an intrinsic spatial resolution of approximately $10\%$0 on both $10\%$1 and $10\%$2 for a $10\%$3 array with $10\%$4 pitch, with $10\%$5 of reconstructed positions within $10\%$6 of the TCT reference. The reconstruction uses amplitude-only features from 12 pads and two random forest regressors with 100 trees each, trained on a position-partitioned 80/20 split (Siviero et al., 2022).

The broader RS4D performance envelope is given in the large-pixel TCT study. At gain $10\%$7, a $10\%$8 pixel achieves a time jitter of $10\%$9 ps and a spatial resolution of $20\%$0 concurrently, while a $20\%$1 pixel achieves $20\%$2 ps and $20\%$3. The paper summarizes the spatial trend as approximately $20\%$4 of pitch at gain $20\%$5, with timing for MIPs remaining in the $20\%$6–$20\%$7 ps range after adding $20\%$8 ps in quadrature (Arcidiacono et al., 2022).

Subsequent work extends the concept from AC-coupled RSD to DC-RSD. The beam-test and TCAD paper on innovative RSD and DC-RSD LGAD devices reports a best position resolution of $20\%$9 micron, about $O(N d)$00 of the $O(N d)$01 pitch, and identifies an optimal n+ sheet resistivity in the range $O(N d)$02–$O(N d)$03 k$O(N d)$04, with low contact resistance of about $O(N d)$05 per pad critical for signal confinement. The paper also studies trench isolation and inter-pad resistive strips as means of controlling cross-talk and preserving 100% fill factor (Moscatelli et al., 14 Aug 2025). A related mixed TCAD+SPICE study states that DC-RSD maintains the key RSD features of excellent timing and spatial resolutions, summarized as few tens of picoseconds and few microns, while eliminating AC-RSD drawbacks such as baseline fluctuation and bipolar tails (Croci et al., 22 Aug 2025).

6. Cross-domain interpretation and disambiguation

The documented usages show that RS4D does not name a unified methodology. In remote sensing, it is a distilled state space model for instance segmentation. In mobile sensing, it is a Butterworth-augmented S4D sequence model. In detector physics, it denotes a hardware concept centered on Resistive Silicon for 4D tracking. In 4D CBCT and 4D radar, it appears as an alias or umbrella shorthand rather than the canonical method name (Yang et al., 24 Jun 2026, Mei et al., 2024, Arcidiacono et al., 2022, Deng et al., 2024, Zheng et al., 21 Mar 2025).

Several recurrent motifs nevertheless appear across these otherwise unrelated uses. One is efficient exploitation of long-range structure: linear-time SSM token mixing in remote sensing, diagonal state space memorization in mobile sensing, whole-series spatiotemporal processing in 4D CBCT, and distributed signal propagation on resistive sheets in detector readout. Another is the coupling of sparse or noisy observations to stronger priors: teacher-student distillation in remote sensing, Butterworth filtering before memorization in mobile sensing, average-image priors and rotational streak separability in CBCT, LiDAR-guided latent diffusion in 4D radar super-resolution, and calibration plus migration-map correction in RSD-based tracking. This suggests that RS4D functions less as a stable acronym than as a compact label repeatedly attached to problems where high-dimensional spatiotemporal structure must be recovered efficiently from constrained measurements.

For technical writing, the safest practice is therefore to expand RS4D at first use and identify the domain explicitly. Without that qualification, the label is ambiguous across at least remote sensing instance segmentation, robust S4D sequence modeling, Resistive Silicon for 4D tracking, informal RSTAR4D shorthand in CBCT, and 4D radar super-resolution research.